Is there any advantage to a new competitor to shoot in multiple organizations, or should I just focus on one at a time?

If you're new to competitive shooting, I'd recommend focusing on one platform at a time, since there's a lot you'll need to learn which has little to do with the gun you're shooting. Sticking with a revolver or semi-auto at first will help you get through this curve faster & better, IMO. It's cheaper, too. Pick the one you shoot best, then start practicing & learning.